1. Field of the Invention
The present invention relates to a measurement apparatus for measuring a surface map (surface shape).
2. Description of the Related Art
Japanese Patent No. 3146590 discloses a prior art of acquiring map data while moving the test surface of a measurement target, and separating the test surface from a system error map by using the acquired map data.
FIG. 2 shows the first measurement position. The first measurement position is set at a position where an optical axis 11 of an optical system, the central position of a test surface 2, and a central axis 10 of the test surface 2 which extends through the center of curvature coincide with each other. FIG. 3 shows the second measurement position. At the second measurement position, the test surface 2 is inclined along a circular arc, that is, the central axis 10 of the test surface 2 is inclined from the optical axis 11 of the optical system by γ.
First, at the first measurement position, the first rotation averaged map is obtained as an average of a plurality of pieces of map data acquired by rotating the test surface. This corresponds to the sum of a system error map and the rotationally invariant components of the test surface.
At the second measurement position, the second rotation averaged map is obtained as an average of a plurality of pieces of map data acquired by rotating the test surface. This corresponds to the sum of the system error map and the rotationally invariant components of the test surface.
When calculating the difference between the first rotation averaged map and second rotation averaged map, the system error map is eliminated, and the difference between the rotationally invariant components of the test surface is obtained. The rotationally invariant components of the map are calculated utilizing the nature of the concentric contours of the rotationally invariant components.
The method of calculating the rotationally invariant components utilizing the nature of the concentric contours will be described with reference to FIG. 4. In FIG. 4, solid lines represent a first rotation averaged map RI1, and broken lines represent a second rotation averaged map RI2. Positions on the same radius of each line form a concentric contour. Positions A and B, and C and D are respectively indicated as RI1A and RI1B on the same contours of the first rotation averaged map. Positions B and D, and A and C are respectively indicated as RI2A and RI2B on the same contours of the second rotation averaged map. FIG. 4 shows the difference between the first rotation averaged map and second rotation averaged map. Accordingly, A, B, C, and D are respectively expressed as RI1A-RI2B, RI1A-RI2A, RI1B-RI2B, and RI1B-RI2A. As four unknowns RI1A, RI1B, RI2A, and RI2B yield three equations, RI1B, RI2A, and RI2B can be obtained with reference to RI1A. When performing the same operation for the entire surface, the rotationally invariant components of the test surface can be obtained.